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Question

I have no idea what I'm doing, please help me.

the intensity of the gravitational field varies inversely as the distance squared. If the intensity is 6 when the distance is 2, what is the intensity when the distance is 3?

I thought it would be 6/9 but .6666 doesn't make sense.

Answer 1

An inverse relationship is given by the formula

xy=k

where x and y are variables, and k is a constant. For our data, let i=intensity of gravitational field and d=distance. Then a formula for our relationship is

id^2=k

We know that when d=2, i=6, and use this information to solve for k:

6*2^2=6*4=24

So k=24. Now we want to know what another i is when d=3. Plug in the information we know:

i*3^2 = 24 -> 9i = 24 -> i = 24/9 -> i = 8/3

Thus, the intensity is 8/3. This makes sense since the greater the distance, the less the intensity.

Answer 2

If the intensity (i) varies inversely as the distance squared (d^2), then you have

i * d^2 = constant.

You are told that the intensity is 6 when the distance is 2, so

6 * 2^2 = 6 * 4 = 24, the constant.

So you now have i * d^2 = 24.

So, if the distance is 3, then

i * 3^2 = 24
i * 9 = 24
i = 24/9 = 8/3, approx. 2.67

Answer 3

The distance has gone up by a factor of (3/2). So since intensity is proportional to the inverse distance squared, we *divide* by (3/2) squared: so 6 / (3/2 * 3/2) = 8/3.

0.6666 makes as much sense as any other number, by the way.

Answer 4

Ah yes... The inverse square law. It applies to anything expanding in a spherical pattern, like light from the sun for instance, or a pressure/shock wave from an explosion.Think a sphere. At 1 unit of distance, a certain amount of light covers 1 square unit on the sphere. At 2 units, the same 1 unit at 1 unit distance now covers 4 units on the 2 unit spehere,and 9 units on the 3 unit distance sphere. So, if there are 6 units on the 2 meter sphere, there are 4/9th of 6 units on the 3 unit sphere, which means 6 units of billliance (intensity) over 9 square units, or 2/3rds per unit on the 3 unit sphere. 0.6667 is the decimal equivalent of 2/3rds, so the answer of 0.6666 is incorrectly rounded, but otherwise correct.

Answer 5

if the intensity of the field is 6 at two, then it's 24 at 1 because if you double 1 (to get back to two, you have to divide by four) Now triple 1 to get to three and you have to divide by 3^2 so 24/9

you could also just have done 6(2/3)^2=6(4/9)=24/9=8/3

Answer 6

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Answer 7

6/(2^2) = x/(3^2)
(6*9)/4 = x
27/2 = x

Answer 8

write out a proportion (2/6 = 3/?) and solve that.

Answer 9

9/4 (6)=14.5

Answer 10

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